the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Cosmogenic nuclide weathering biases: Corrections and potential for denudation and weathering rate measurements
- 1GFZ German Centre for Geoscience Research, Potsdam, Germany
- 2Department of Geosciences, Colorado State University, Fort Collins, CO, U.S.A.
- 3Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, Purdue, IN, U.S.A.
- 1GFZ German Centre for Geoscience Research, Potsdam, Germany
- 2Department of Geosciences, Colorado State University, Fort Collins, CO, U.S.A.
- 3Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, Purdue, IN, U.S.A.
Abstract. Cosmogenic radionuclides (CRNs) are the standard tool to derive centennial-to-millennial timescale denudation rates, however, it has been demonstrated that chemical weathering in some settings can bias CRNs as a proxy for landscape denudation. Currently, studies investigating CRN weathering biases have mostly focused on the largely insoluble target mineral quartz in felsic lithologies. Here, we examine the response of CRN build-up for both soluble and insoluble target minerals under different weathering scenarios. We assume a simple box model in which bedrock is converted to regolith at a constant rate, and denudation occurs by regolith erosion and weathering either in the regolith or along the regolith-bedrock interface, as is common in carbonate bedrock. We show that weathering along the regolith-bedrock interface increases CRN concentrations compared to a no-weathering case, and how independently derived weathering rates or degrees can be used to correct for this bias. If weathering is concentrated within the regolith, insoluble target minerals will have a longer regolith residence time and higher nuclide concentration than soluble target minerals. This bias can be identified and corrected using paired nuclide measurements coupled with knowledge of either the bedrock or regolith mineralogy to derive denudation and long-term weathering rates. Similarly, single nuclide denudation measurements can be corrected if a weathering rate and compositional data are available. Our model highlights that for soluble target minerals, the relationship between nuclide accumulation and denudation is not monotonic. We use this understanding to map the conditions of regolith mass, weathering, and denudation rates at which weathering corrections for cosmogenic nuclides become large and ambiguous as well as identify environments in which the bias is mostly negligible, and CRN concentrations reliably reflect landscape denudation. We highlight how measurements of CRNs from soluble target minerals, coupled with bedrock and regolith mineralogy, can help to expand the range of landscapes for which centennial-to-millennial timescale denudation and weathering rates can be obtained.
Richard F. Ott et al.
Status: final response (author comments only)
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RC1: 'Comment on gchron-2022-5', Anonymous Referee #1, 19 Apr 2022
This is a fascinating and useful study of the effects of target solubility on CRN concentrations in a weathering substrate. The authors clearly present the theoretical underpinning and build up a model of target mineral enrichment/depletion in the weathered substrate. They additionally show that multiple weathering proxies can be used to correct for enrichment/depletion for basin-wide studies, which will be of broad interest. Using the WeCode package in advance of fieldwork will certainly be of benefit as well. Overall, this is a well-written manuscript and an excellent contribution to the field. I do have some concerns and points of clarification that I hope the authors will consider.
The basic conceptual model requires a mixed and eroding regolith. This is illustrated in figure 2, but it would be worth highlighting this and discussing the potential pitfalls that researchers might run into if this assumption is violated (i.e mixed but not eroding, or eroding but not well mixed).
The variable k requires some extra discussion. It is defined on line 175 as a function of changing grain mass through time. I am guessing this is derived from the weathering rates? In any case, the manuscript could use a fuller discussion of how to derive k.
Line 124-126: why was radioactive decay ignored? As the authors point out, this is not likely a problem for 10Be, but 14C is becoming a common tool for quartz-based studies, especially in complex erosional settings where this technique will undoubtedly be used. Since the authors must have used some form of the nuclide production equation, I would think it should not be too difficult to put the decay term back in.
Table 1 is missing mg, mi, and k. (k is the most important)
Lines 183-185: I am struggling with the idea that the average grain residence time is always longer than the residence time of a parcel of rock. This is justified with equation 8, but this feels a bit like Zeno’s paradox where you can never be shot with an arrow since it will always travel half the remaining distance. For soluble target minerals at low erosion rates, there must be a point where all that mineral has dissolved away before the original parent rock has moved through the regolith. It is possible that this is a function of the assumption of a mixed-eroding regolith. If so, that should be clearly stated.
It would be helpful to the reader to reiterate that IR and IB are mineral fractions and not concentrations.
The unknowable errors that are mentioned on lines 290-292 are potentially very large. These could be partially addressed by expanding on the implications of the model assumptions as mentioned above.
Line 307: ‘corrected denudation rate’ = input?
Section 5.2 could be focused a bit more to remove repetition from earlier.
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AC1: 'Reply on RC1', Richard Ott, 02 May 2022
We thank the reviewer for the feedback and constructive comments that will improve the manuscript. We agree with the reviewer that including radioactive decay will make the study more widely applicable and will include decay into the revised manuscript and associated codes. The nuclide build-up equations with radioactive decay are harder to follow compared to the no-decay version. We will therefore keep the no-decay equations in the main text and add all equations with decay as a supplement.
The revised version will also include a brief discussion of the mixing assumption and the expectations in a no mixing setting. In addition, we will explain in more detail the role and derivation of the grain mass weathering constant k.
Regarding the comments on Line 183-185. The average residence time of a parcel of rock always has to be equal or longer than the average grain residence time of soluble minerals in a homogeneous bedrock. In case where there is only erosion (i.e., no chemical weathering), both residence times will be equal. In a case where we have the same denudation rate but it is partitioned into 50% erosion and 50% chemical weathering, mass is removed at the same rate as in the no weathering case, but the mechanical removal of grains by erosion is 50% slower. This behavior would also occur if the regolith were not mixed, but weathering took place throughout the regolith. The fact that in Eq.8, a grain will never fully weather away is just a consequence of using a weathering law, where the mass loss is proportional to grain mass. In a low denudation, high weathering scenario, this would lead to some very small grains that have been sitting in the regolith for a long time. We agree that, in reality, many of these grains will fully dissolve instead of becoming infinitesimally small, but for capturing the general behavior of grain size effects on the average regolith nuclide concentration, this does not matter because they do not contribute a significant mass to the regolith.
We also thank the reviewer for their line-by-line comments. These are insightful and will be incorporated into the manuscript during the revision process.
We will detail our responses to these and other points in our line-by-line responses to both reviewers that will be posted with our revised submission.
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AC1: 'Reply on RC1', Richard Ott, 02 May 2022
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RC2: 'Comment on gchron-2022-5', Claire E Lukens, 24 Apr 2022
Ott et al. provide a solid theoretical framework for addressing weathering biases in denudation rate studies using soluble target minerals. This work expands on established literature that has been focused largely on insoluble minerals, and provides transparent, adaptable, and publically-available code that implements their approach. This work is timely, and includes a paired nuclide approach that should be useful for expanding into understudied landscapes. The manuscript is well-written, and the figures are (mostly - see below) clear and helpful.
Re: Ignoring radioactive decay: How did you determine what was “acceptable” for the residence time thresholds given here? Is this the time over which ignoring decay would introduce a 5% error? More error than the analytical error? It feels a bit nitpicky, but being a bit more specific about what is deemed acceptable will help others implementing your code decide if ignoring radioactive decay is acceptable in their particular system. Especially for 36Cland 14C systems, decay could be worth considering in many systems. Adding it to the code seems like a relatively straightforward thing to implement, and would make the approach broadly applicable across a wider range of settings, including weathering studies outside of active tectonic settings. I certainly don’t see adding decay to the code as a requirement for publication at this time, but it would be good to be clear about how big the impacts are for studies at the edges of the “acceptable” ranges given here.
The discussion on possible grain size effects was very interesting. It makes sense to me that even without any grainsize-dependent sediment transport, size reduction of grains due to weathering and the associated range of particle residence times could introduce a relationship between particle size and CRN concentration. What’s not clear from this conceptual framework is whether this effect will be large enough to worry about given all the other assumptions and sources of error. I’d love to see a full-blown model treatment to evaluate the possible magnitude of grain size effects in the context of other sources of error, but that’s certainly beyond the scope here.
Minor comments:
In figure 5, it would be helpful to define XR/XB in the caption, especially for readers who are skimming figures before they get into the meat of the text (or readers like me who get easily lost in variable alphabet soup when I’m tired)
Line 285: “regolith is relatively thick (200 g/cm2)” – I assume from the units that this is an attenutation length, not a regolith thickness?
Figure 6: because the examples here use different nuclides, it would be easy to readers to be confused about the different between the scenarios. Just looking at the figure, it’s easy to assume that scenario 1 is for 10Be, scenario 2 is for 36Cl, and scenario 3 is for both. Either 10Be or 36Cl would give the same result in (a), correct? You might consider just using 36Cl as the example in both (a) or (b), or hammering home that point in the caption.
Lines 374-375: “finding the denudation rate with the maximum nuclide concentration” and in the next sentence: solving for the maximum denudation rate – I’m confused, won’t these be opposite (high CRN concentration = low denudation rate). Do you mean minimum D here? The notation around DNmax is also a bit confusing, since it’s a low denudation rate with “max” in the subscript. I think I understand why it was notated that way, but this section required super close reading to make sure I didn’t get lost.
There are a few minor typos and formatting things annotated in the attached PDF.
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AC2: 'Reply on RC2', Richard Ott, 02 May 2022
We thank the reviewer for the feedback and constructive comments that will improve the manuscript. We agree with the reviewer that including radioactive decay will make the study more widely applicable and will include decay in the revised manuscript and associated codes. The nuclide build-up equations with radioactive decay are harder to follow compared to the no-decay version. We will therefore keep the no-decay equations in the main text and add all equations with decay as a supplement.
We agree with the reviewer that the grain size effects of weathering are interesting and deserve more investigation beyond the scope of this manuscript. We assume that in areas of low denudation rate and high weathering, the grain size bias may be a major source of error. Calculating the magnitude of the bias requires knowledge of the grain size distribution entering the regolith and the grain size distribution within the regolith. Doing so requires observational constraints that, to our knowledge, currently do not exist. However, this suggestion highlights a critical area of future research.
We thank the reviewer for their detailed line-by-line comments and manuscript annotations. These are very helpful and will be incorporated into the manuscript during the revision process.
We will detail our responses to these and other points in our line-by-line responses to both reviewers that will be posted with our revised submission.
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AC2: 'Reply on RC2', Richard Ott, 02 May 2022
Richard F. Ott et al.
Data sets
WeCode v1.0 - Weathering Corrections for denudation rates Ott, Richard https://dataservices.gfz-potsdam.de/panmetaworks/review/6070fc0104aed0a59bc47a2eda6260cf95ec1a09377fdf5bbc382a74cc52926f/
Richard F. Ott et al.
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